Ellsberg's (1961) famous paradox shows that decision-makers give events with ‘known’ probabilities a higher weight in their outcome evaluation. In the same article, Ellsberg suggests a preference representation which has intuitive appeal but lacks an axiomatic foundation. Schmeidler (1989) and Gilboa (1987) provide an axiomatisation for expected utility with non-additive probabilities. This paper introduces E-capacities as a representation of beliefs which incorporates objective information about the probability of events. It can be shown that the Choquet integral of an E-capacity is (...) the Ellsberg representation. The paper further explores properties of this representation of beliefs and provides an axiomatisation for them. (shrink)

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.